At a Manhattan hotel, the New York property developer said his vice presidential pick was a “solid” man, BBC reported on Saturday.
He tried to dispel reports that he had been conflicted about his choice by insisting the 57-year-old governor was definitely his first choice.
Pence is well known for his strong socially-conservative credentials.
The governor joined Trump on stage and described him as “a good man” who “will make a great president”.
Trump will be formally made the Republican presidential candidate at the party’s national convention in Cleveland next week.
Trump praised his vice presidential choice as man who had served “with distinction” in Congress equipped with “the skills of a highly talented executive”.
“I introduce a man who I truly believe will be outstanding in every way and who will be the next vice president of the United States, Governor Mike Pence,” he said.
Their joint appearance on Friday was rescheduled after the lorry attack in France, amid reports that Trump only settled on Pence after being talked out of other options by his family.